Finite Group DatabasebetaFinite Group Databasebeta| order | 5392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#13062438 |
| unambiguous semidirect product | (C2×#13062438)⋊C2 |
| Fitting | C22×C337 ⋊ C4 |
| Sylow | C337 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#13062438 |
| commutator, socle | C2×C337 | C2×C4 |
| Fitting | C22×C337 | C4 |
| hypercenter | C22 | #13062438 |
| hypocenter | C337 | C22⋊C4 |
| LCS | G ▷ C2×C337 ▷ C337 | |
| UCS | C1 ◁ C2 ◁ C22 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,337|a^2=d,b^a=bc,e^a=e^148,e^d=e^336346 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5392, 45);